Basic Math Examples

$| 7 - 3 t | = 8$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$7 - 3 t = \pm 8$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$7 - 3 t = 8$

Step 2.2

Move all terms not containing $t$ to the right side of the equation.

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Step 2.2.1

Subtract $7$ from both sides of the equation.

$- 3 t = 8 - 7$

Step 2.2.2

Subtract $7$ from $8$ .

$- 3 t = 1$

Step 2.3

Divide each term in $- 3 t = 1$ by $- 3$ and simplify.

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Step 2.3.1

Divide each term in $- 3 t = 1$ by $- 3$ .

$\frac{- 3 t}{- 3} = \frac{1}{- 3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 3 t}{- 3} = \frac{1}{- 3}$

Step 2.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{1}{- 3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

$t = - \frac{1}{3}$

Step 2.4

Next, use the negative value of the $\pm$ to find the second solution.

$7 - 3 t = - 8$

Step 2.5

Move all terms not containing $t$ to the right side of the equation.

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Step 2.5.1

Subtract $7$ from both sides of the equation.

$- 3 t = - 8 - 7$

Step 2.5.2

Subtract $7$ from $- 8$ .

$- 3 t = - 15$

Step 2.6

Divide each term in $- 3 t = - 15$ by $- 3$ and simplify.

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Step 2.6.1

Divide each term in $- 3 t = - 15$ by $- 3$ .

$\frac{- 3 t}{- 3} = \frac{- 15}{- 3}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $- 3$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{- 3 t}{- 3} = \frac{- 15}{- 3}$

Step 2.6.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 15}{- 3}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide $- 15$ by $- 3$ .

$t = 5$

Step 2.7

The complete solution is the result of both the positive and negative portions of the solution.

$t = - \frac{1}{3}, 5$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{1}{3}, 5$

Decimal Form:

$t = - 0.\overline{3}, 5$